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Weighted recursive cube-mask surface helpers

Source: R/export_examples.R, R/graph_helpers.R
recursive_cube_mask_surface_helpers.Rd

Convenience helpers that recursively subdivide a cube into a regular \(k \times k \times k\) array of subcubes according to a cubic keep-mask, retain the selected cells at each recursion step, and deform the resulting face-adjacency graph inside \(\mathbb{R}^3\). This provides a generic cubical 3D family that includes Menger-sponge-style cell adjacency as a named special case.

Usage

recursive.cube.mask.surface.graph(
  mask,
  level = 2,
  surface = c("standard", "bulged", "twisted", "wavy"),
  amplitude = 0.2,
  freq = 2,
  twist = 0.6,
  x.scale = 1,
  y.scale = 1,
  z.scale = 1,
  normalize = c("median", "mean", "none")
)

Arguments

mask

Cubic logical or numeric keep-array. Non-zero entries are retained at each recursive step.

level

Recursion depth. Must be at least 1.

surface

Cube-mask geometry family. One of "standard", "bulged", "twisted", or "wavy".

amplitude

Finite deformation amplitude.

freq

Positive modulation frequency used only when surface = "wavy".

twist

Finite twist strength used only when surface = "twisted".

x.scale

Positive horizontal scaling applied to the canonical cube coordinates.

y.scale

Positive vertical scaling applied to the canonical cube coordinates.

z.scale

Positive depth scaling applied to the canonical cube coordinates.

normalize

Normalization applied to the induced edge lengths. One of "median", "mean", or "none".

Value

The coords_surface component is an n x 3 numeric matrix with columns x, y, and z.

recursive.cube.mask.surface.graph() returns a list with components:

  • edges: the retained recursive cube-mask face-adjacency edges,

  • n: number of vertices,

  • edge_weights: induced positive edge lengths,

  • coords_surface: the 3D embedding,

  • coords_param: the canonical 3D voxel-center coordinates,

  • weight_scale: the normalization constant applied to the raw edge lengths,

  • family: always "recursive.cube.mask",

  • surface: the chosen surface name,

  • level: the recursion depth,

  • mask: the logical keep-array,

  • mask_side: side length of the base keep-mask,

  • side: side length of the fully refined cube grid,

  • label: a human-readable family label.

Details

The mask is interpreted as a cubic array whose first dimension runs from top to bottom, second from left to right, and third from front to back. Non-zero entries are retained at each recursive step.

Examples

mask <- mask.cube.channel.network(
  side = 5, channel.width = 1, branch.offset = 2
)
cube <- recursive.cube.mask.surface.graph(mask, level = 1)